We approximate quantum annealing with classical path-integral Monte Carlo method described in Section REF .
The SQA procedure assumes a Chimera graph where the total number of qubits is \(b\) .
For the quantum annealing Hamiltonian \({\mathbf {H}}_D(t)\)  in (REF ), to find the Boltzmann state of the quantum system, we are required to evaluate canonical partition function \(\text{tr}[e^{-\mathbf {H}_D(t)/T}]\)  for the transverse field quantum Ising model.
To approximate the partition function, we use the Trotter formula [1]}, [2]}, [3]}.
Specifically, given annealing schedules \(A(t)\)  and \(B(t)\)  from quantum annealing and to approximate the partition function for quantum annealing Hamiltonian \({\mathbf {H}}_D(t)\)  with temperature \(T\) , we replace the temperature parameter by \(T/B(t)\)  and the transverse field parameter by \(A(t)/B(t)\) .
Such approximation maps the transverse quantum Ising model to a classical \((2+1)\) -dimensional anisotropic Ising model with temperature \(\tau T\)  and Hamiltonian
\({\mathbf {H}}^c_{aI}(\mathbf {s})=-\sum \limits _{l=1}^\tau \left[ B(t) \sum _{(i,j) \in \cal E (\cal G)} J_{ij} s_{il} s_{jl} +J(t) \sum _{j \in \cal V (\cal G)} s_{jl}s_{j, l+1} \right]\) 
